Can Gamma-Ray Bursts Be Used to Measure Cosmology? A Further Analysis

Three different methods of measuring cosmology with gamma-ray bursts (GRBs) have been proposed since a relation between the gamma-ray energy Eg of a GRB jet and the peak energy E sub(p) of the vF sub(v) spectrum in the burst frame was reported by Ghirlanda and coauthors. In method I, to calculate the probability for a favored cosmology, only the contribution of the E sub(g)-E sub(p) relation that is already best-fitted for this cosmology is considered. We apply this method to a sample of 17 GRBs and obtain the mass density sub(M)=0.15 super(+) sub(-) super(0) sub(0) super(.) sub(.) super(4) sub(1) super(5) sub(3) (1 s) for a flat CDM universe. In method II, to calculate the probability for some certain cosmology, contributions of all the possible E sub(g)-E sub(p) relations that are best-fitted for their corresponding cosmologies are taken into account. With this method, we find a constraint on the mass density 0.14 < sub(M) < 0.69 (1 s) for a flat universe. In method III, to obtain the probability for some cosmology, contributions of all the possible E sub(g)-E sub(p) relations associated with their unequal weights are considered. With this method, we obtain an inspiring constraint on the mass density 0.16 < sub(M) < 0.45 (1 s) for a flat universe and x super(2)dof = 19.08/15 = 1.27 for the concordance model of sub(M)= 0.27. Compared with the previous two methods, method III makes the observed 17 GRBs place much more stringent confidence intervals at the same confidence levels. Furthermore, we perform a Monte Carlo simulation and use a larger sample to investigate the cosmographic capabilities of GRBs with different methods. We find that a larger GRB sample could be used to effectively measure cosmology, no matter whether the E g-E sub(p) relation is calibrated by low-z bursts or not. Ongoing observations of GRBs in the Swift era are expected to make the cosmological utility of GRBs progress from its babyhood into childhood.